Algebraic & Geometric Topology Volume 13, issue 2 (2013)

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Group completion and units in $\mathcal{I}\mkern -1mu$–spaces

Steffen Sagave and Christian Schlichtkrull

Algebraic & Geometric Topology 13 (2013) 625–686

DOI: 10.2140/agt.2013.13.625

Bibliography

1	M Ando, A J Blumberg, D J Gepner, M J Hopkins, C Rezk, Units of ring spectra and Thom spectra arXiv:0810.4535
2	M Basterra, André–Quillen cohomology of commutative $S$–algebras, J. Pure Appl. Algebra 144 (1999) 111 MR1732625
3	M Basterra, M A Mandell, Homology and cohomology of $E_\infty$ ring spectra, Math. Z. 249 (2005) 903 MR2126222
4	A J Blumberg, R L Cohen, C Schlichtkrull, Topological Hochschild homology of Thom spectra and the free loop space, Geom. Topol. 14 (2010) 1165 MR2651551
5	J M Boardman, R M Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Math. 347, Springer (1973) MR0420609
6	M Bökstedt, Topological Hochschild homology, preprint (1985)
7	A K Bousfield, On the telescopic homotopy theory of spaces, Trans. Amer. Math. Soc. 353 (2001) 2391 MR1814075
8	A K Bousfield, E M Friedlander, Homotopy theory of $\Gamma $–spaces, spectra, and bisimplicial sets, from: "Geometric applications of homotopy theory, II" (editors M G Barratt, M E Mahowald), Lecture Notes in Math. 658, Springer (1978) 80 MR513569
9	A K Bousfield, D M Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. 304, Springer (1972) MR0365573
10	A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Math. Surveys and Monographs 47, Amer. Math. Soc. (1997) MR1417719
11	P G Goerss, J F Jardine, Simplicial homotopy theory, Progress in Mathematics 174, Birkhäuser (1999) MR1711612
12	P S Hirschhorn, Model categories and their localizations, Math. Surveys and Monographs 99, Amer. Math. Soc. (2003) MR1944041
13	M Hovey, Model categories, Math. Surveys and Monographs 63, Amer. Math. Soc. (1999) MR1650134
14	M Hovey, Spectra and symmetric spectra in general model categories, J. Pure Appl. Algebra 165 (2001) 63 MR1860878
15	M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
16	J Lind, Diagram spaces, diagram spectra, and spectra of units arXiv:0908.1092
17	S Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer (1998) MR1712872
18	M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. 82 (2001) 441 MR1806878
19	J P May, The geometry of iterated loop spaces, Lectures Notes in Math. 271, Springer (1972) MR0420610
20	J P May, $E_{\infty }$ spaces, group completions, and permutative categories, from: "New developments in topology" (editor G Segal), London Math. Soc. Lecture Note Ser. 11, Cambridge Univ. Press (1974) 61 MR0339152
21	J Rognes, Topological logarithmic structures, from: "New topological contexts for Galois theory and algebraic geometry" (editors A Baker, B Richter), Geom. Topol. Monogr. 16 (2009) 401 MR2544395
22	S Sagave, C Schlichtkrull, Diagram spaces and symmetric spectra, Adv. Math. 231 (2012) 2116 MR2964635
23	R Santhanam, Units of equivariant ring spectra, Algebr. Geom. Topol. 11 (2011) 1361 MR2821427
24	C Schlichtkrull, Units of ring spectra and their traces in algebraic $K$–theory, Geom. Topol. 8 (2004) 645 MR2057776
25	C Schlichtkrull, The homotopy infinite symmetric product represents stable homotopy, Algebr. Geom. Topol. 7 (2007) 1963 MR2366183
26	C Schlichtkrull, Thom spectra that are symmetric spectra, Doc. Math. 14 (2009) 699 MR2578805
27	C Schlichtkrull, Higher topological Hochschild homology of Thom spectra, J. Topol. 4 (2011) 161 MR2783381
28	S Schwede, Symmetric spectra
29	S Schwede, Stable homotopical algebra and $\Gamma$–spaces, Math. Proc. Cambridge Philos. Soc. 126 (1999) 329 MR1670249
30	S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. 80 (2000) 491 MR1734325
31	S Schwede, B Shipley, A uniqueness theorem for stable homotopy theory, Math. Z. 239 (2002) 803 MR1902062
32	G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR0353298
33	B Shipley, Symmetric spectra and topological Hochschild homology, $K$–Theory 19 (2000) 155 MR1740756
34	R W Thomason, Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979) 91 MR510404